Ultrasonic inspections of reactor in-vessel components are of ten performed remotely under difficult circumstances requiring complex and expensive manipulators to position one or more transducers near the surf ace of the component. The transducers then scan over a portion of the surface to image any flaws in the volume scanned. Usually, there are regions of the reactor internals that are inaccessible to the relatively large manipulator arm, limiting the ability to fully inspect, for example, some important portions of the vessel wall, in-core and control-rod-drive housings, and stub tubes.
One difficulty encountered is placement of the transducer close to, or in contact with, the inspection surface. In-vessel inspections are conducted with submersible transducers that usually require a proximate hardened electronics package for pulsing and detection purposes. Some transducers require a relatively proximate preamplifier. The design and construction of electronics packages that can withstand gamma radiation emanating f rom the reactor core has been successfully undertaken, but cost savings would result if such novel designs were unnecessary. Rather, some inexpensive and compact means of transporting the sonic energy between a central location and a remote inspection surface would simplify the design and operation of in-vessel, as well as other, inspection systems.
Ultrasonic waveguides are known which comprise thin metal rods. However, such rods are not very flexible, making them undesirable for use in inspecting components of nuclear reactors having surf aces which are difficult to access. Also, such metal rods are very inefficient due to the severe attenuation of the ultrasonic waves, especially shear mode waves, in the metal. This problem led to consideration of fluid-filled thin-walled tubes to transport ultrasonic energy.
Ultrasonic waves propagating in fluids are essentially compressive in nature. The fluid motion is parallel to the direction of propagation, just like longitudinal waves in solids. Such waves usually diverge spherically from small point-like sources, and the intensity obeys the inverse-square law. However, in the presence of a solid boundary of cylindrical shape, i.e., a duct, the waves traveling in a viscous fluid can be propagated in certain modes of differing axial symmetry. The waves are damped in time and space as they propagate, depending on the properties of the fluid and duct, the duct dimensions and the wave frequency. In fact, damping is most appreciable for shear-wave motion of the fluid, confined to the boundary layer near the solid walls.
A lengthy and in-depth analysis of the free vibration of a thin-walled cylindrical waveguide filled with a compressible viscous fluid has been performed using the linearized Navier-Stokes equations [see, L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Addison-Wesley, Reading, (1959)], the fluid continuity equation and Flugge's equations of motion for thin shells [see, W. Flugge, Stresses in Shells, Springer-Verlag, Berlin, (1960)]. Unique solutions can be obtained for which the interface conditions at the waveguide inner surface can be satisfied. Formally, a characteristic equation for the system eigenvalues can be formulated and a numerical solution can be derived. [see, T. T. Yeh and S. S. Chem, "Dynamics of a Cylindrical Shell system coupled by Viscous Fluid", J. Acost. Soc. Am., Vol., 62, No. 2, 262-270 (1977) and G. B. Warburton, "Vibration of a Cylindrical Shell in an Acoustic Medium," J. Mech. Eng. Sc., Vol. 3, No. 1, 69-79 (1961).]
It can be shown that a solution exists for guided wave modes in the special case of axi-symmetric propagation. The characteristic equation can be solved numerically in this case, resulting in a dispersion equation for axial wave propagation. [See, J. H. Terhune and K. Karim-Panahi, "Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell", Proc. ASME PV&P Conf., New Orleans, Vol. 231, 41-50 (1992).]